Fundamentals
The core facts every aspirant should own — each a titled nugget with a real-world story, the concept in plain words, and a memory trick. Works even when the internet doesn't.
1,200 fundamentals
“They're just conservation of charge and energy dressed up for circuits.”
Junction rule: charge is conserved (currents in = out). Loop rule: energy is conserved (voltage gains = drops).
Memory trick: Junction = charge; loop = energy.
“A heater's thick coil and high current turn electrical energy into cosy heat.”
Power dissipated P = VI = I²R = V²/R.
P = VI
Memory trick: P = VI.
“A weak battery reads fine until you draw current — then its voltage sags.”
EMF is a cell's full push; terminal voltage is what remains after the internal resistance drops some of it.
Memory trick: Terminal V = EMF − Ir.
“This sideways push bends particle beams in old TV tubes and particle accelerators.”
A magnetic field exerts F = qvB sinθ on a moving charge, always perpendicular to its velocity.
F = qvB sinθ
Memory trick: Magnetic force does no work.
“Wiggle a magnet near a coil and you generate electricity — the basis of every generator.”
A changing magnetic flux induces an EMF, EMF = −dΦ/dt.
EMF = −dΦ/dt
Memory trick: Only a CHANGING flux induces.
“Drop a magnet down a copper pipe and it falls in slow motion, braked by induced currents.”
The induced current opposes the change that created it — conserving energy.
Memory trick: Nature resists the change.
“Power lines ship electricity at high voltage, then transformers step it down for your home.”
Transformers change AC voltage using the ratio of coil turns; they don't work on DC.
Vₛ/Vₚ = Nₛ/Nₚ
Memory trick: Turns ratio sets voltage ratio.
“Coal, water or wind all do one job: spin a coil to make AC.”
Rotating a coil in a magnetic field induces alternating EMF — the heart of power stations.
Memory trick: Spin a coil → AC.
“It's why a mirror gives you a clean, predictable image.”
The angle of incidence equals the angle of reflection, and both lie in one plane.
Memory trick: Angle in = angle out.
“A straw looks broken at the water's surface because light bends as it exits.”
Light bends at a boundary: n₁ sinθ₁ = n₂ sinθ₂.
n₁sinθ₁ = n₂sinθ₂
Memory trick: Into denser medium → bends toward normal.
“Optical fibres pipe internet light across oceans using total internal reflection.”
Beyond the critical angle, light in a denser medium reflects completely instead of refracting.
Memory trick: Dense→rare, past critical angle → all reflects.
“Your eye's lens changes shape to keep u, v and f in balance so images land on the retina.”
For a thin lens, 1/v − 1/u = 1/f.
1/v − 1/u = 1/f
Memory trick: Mind the sign convention.
“A magnifying glass is convex; glasses for short sight are concave.”
A convex lens converges light (used for magnifying, farsight); a concave lens diverges it (used for nearsight).
Memory trick: Convex converges; concave diverges.
“Rainbows are raindrops acting as millions of tiny prisms.”
A prism splits white light into colours because each colour refracts by a different amount.
Memory trick: Violet bends most, red least.
“The striped pattern was the experiment that convinced physicists light behaves as a wave.”
Overlapping light waves from two slits interfere, making bright and dark fringes — proof light is a wave.
β = λD/d
Memory trick: Fringe width β = λD/d.
“Einstein won his Nobel for explaining this — proof that light comes in packets.”
Light ejects electrons from a metal only above a threshold frequency, regardless of intensity.
Memory trick: Frequency decides IF; intensity decides HOW MANY.
“Bluer light carries more energetic photons than red — which is why UV can burn your skin.”
Light comes in quanta of energy E = hf = hc/λ.
E = hf
Memory trick: Higher frequency → more energetic photon.
“Neon signs glow because electrons jump between these fixed rungs, emitting exact colours.”
Electrons occupy fixed energy levels; for hydrogen Eₙ = −13.6/n² eV.
Eₙ = −13.6/n² eV
Memory trick: Bound electron → negative energy.
“Electron microscopes exploit the electron's tiny wavelength to see viruses.”
Every particle has a wavelength λ = h/p, noticeable only for tiny masses.
λ = h/p
Memory trick: Matter waves matter only at atomic scale.
“The Sun shines by converting a little mass into enormous energy every second.”
Mass and energy are interchangeable via E = mc².
E = mc²
Memory trick: A tiny mass → huge energy (c² is vast).
“Fission powers today's reactors; fusion is the Sun's engine we're trying to bottle.”
Fission splits heavy nuclei (reactors, bombs); fusion joins light nuclei (the Sun) — both release energy.
Memory trick: Split heavy / join light → energy.
“Carbon-14's 5,730-year half-life lets us date ancient bones and artefacts.”
The time for half the nuclei in a sample to decay; constant for a given isotope.
Memory trick: Half gone each half-life, always.
“Joining the two makes a diode — the on/off valve behind all electronics.”
n-type is doped for extra free electrons; p-type for holes (missing electrons).
Memory trick: n = negative carriers; p = positive holes.
“Chargers use diodes to turn wall AC into the DC your phone needs.”
A diode lets current flow easily one way and blocks the other.
Memory trick: One-way valve for current.